This medieval style acorn hat is made of wool, lined with linen and sewn in to shape.
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Acorn hats in addition to being acorn-shaped, have a little pip of fabric at the top that in the case of acorn hat probably represent the stalk or possibly the remains of the style.
The pip also occurs through the felting process if this were a felted, rather sewn acorn hat.
Looking at the pictures I think this hat needs more air time or ironing, its been crushed in the bottom of bag too long and never seem to see the light of day.